What would be the equation of an elliptical paraboloid which sits on XZ plane?
$begingroup$
$f(x, y) = -x^2-y^2+4$ is the equation of a paraboloid which sits on the XY plane and protrudes toward Z-axis.
See the link.
So, if I want a paraboloid to be drawn on the surface XZ, I should write: $f(x, z) = -x^2-z^2+4$
My question is, is it possible to write an equation of a paraboloid as a function of x,y, even though it sits on the surface XZ?
Why or why not?
functions graphing-functions
edited Dec 27 '18 at 23:56
Bernard
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
$endgroup$
add a comment |
$begingroup$
$f(x, y) = -x^2-y^2+4$ is the equation of a paraboloid which sits on the XY plane and protrudes toward Z-axis.
See the link.
So, if I want a paraboloid to be drawn on the surface XZ, I should write: $f(x, z) = -x^2-z^2+4$
My question is, is it possible to write an equation of a paraboloid as a function of x,y, even though it sits on the surface XZ?
Why or why not?
functions graphing-functions
edited Dec 27 '18 at 23:56
Bernard
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
$endgroup$
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21
add a comment |
$begingroup$
$f(x, y) = -x^2-y^2+4$ is the equation of a paraboloid which sits on the XY plane and protrudes toward Z-axis.
See the link.
So, if I want a paraboloid to be drawn on the surface XZ, I should write: $f(x, z) = -x^2-z^2+4$
My question is, is it possible to write an equation of a paraboloid as a function of x,y, even though it sits on the surface XZ?
Why or why not?
functions graphing-functions
edited Dec 27 '18 at 23:56
Bernard
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
$endgroup$
$f(x, y) = -x^2-y^2+4$ is the equation of a paraboloid which sits on the XY plane and protrudes toward Z-axis.
See the link.
So, if I want a paraboloid to be drawn on the surface XZ, I should write: $f(x, z) = -x^2-z^2+4$
My question is, is it possible to write an equation of a paraboloid as a function of x,y, even though it sits on the surface XZ?
Why or why not?
functions graphing-functions
functions graphing-functions
edited Dec 27 '18 at 23:56
Bernard
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
edited Dec 27 '18 at 23:56
Bernard
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
edited Dec 27 '18 at 23:56
Bernard
124k742117
edited Dec 27 '18 at 23:56
Bernard
124k742117
edited Dec 27 '18 at 23:56
Bernard
124k742117
124k742117
asked Dec 27 '18 at 23:53
user366312user366312
648519
asked Dec 27 '18 at 23:53
user366312user366312
648519
asked Dec 27 '18 at 23:53
user366312user366312
648519
648519
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21
add a comment |
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3054455%2fwhat-would-be-the-equation-of-an-elliptical-paraboloid-which-sits-on-xz-plane%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3054455%2fwhat-would-be-the-equation-of-an-elliptical-paraboloid-which-sits-on-xz-plane%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
It is not a function, it consists of two braches. $$y = -x^2 -z^2 + 4 iff z^2 = 4 - y - x^2 implies z = pm sqrt{4 - y -x^2}$$ To visualize, you can plot individual branch instead.
$endgroup$
– achille hui
Dec 28 '18 at 0:27
$begingroup$
No more than you can write $y$ as a function of $x$ for a parabola that opens in the direction of the $x$-axis.
$endgroup$
– amd
Dec 28 '18 at 1:21